On sprays with vanishing χ-curvature
Zhongmin Shen
Abstract
Every Riemannian metric or Finsler metric on a manifold induces a spray via its geodesics. In this paper, we discuss several expressions for the [Formula: see text]-curvature of a spray. We show that the sprays obtained by a projective deformation using the S-curvature always have vanishing [Formula: see text]-curvature. Then we establish the Beltrami Theorem for sprays with [Formula: see text].
Topics & Concepts
MathematicsCurvatureGeodesicMetric (unit)Pure mathematicsRicci curvatureScalar curvatureManifold (fluid mechanics)Sectional curvatureFinsler manifoldMathematical analysisGeometryEconomicsEngineeringMechanical engineeringOperations managementAdvanced Differential Geometry Research